Global sensitivity analysis for multivariate outputs based on multiple response Gaussian process model

The computational models in real-world applications commonly have multivariate dependent outputs of interest, and developing global sensitivity analysis techniques, so as to measure the effect of each input variable on each output as well as their dependence structure, has become a critical task. In this paper, a new moment-independent sensitivity index is firstly developed for quantifying the effect of each input variable on the dependence structure of model outputs. Then, the multiple response Gaussian process (MRGP) surrogate model with separable covariance is introduced for efficiently estimating the existing sensitivity indices for multiple response models and the newly developed one. Some indices are analytically derived based on the hyper-parameters of the MRGP model, while others are numerically estimated. One numerical example and three engineering examples are introduced to compare the newly developed sensitivity index with the classical ones, and to demonstrate the effectiveness of the MRGP-based method in estimating these sensitivity indices.